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Approach regions for the square root of the Poisson kernel and bounded functions

Published online by Cambridge University Press:  17 April 2009

P. Sjögren
P. Sjögren
Affiliation:
Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412 96 GöteborgSweden email: peters@math.chalmers.se
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If the Poisson kernel of the unit disc is replaced by its square root, it is known that normalised Poisson integrals of Lp boundary functions converge almost everywhere at the boundary, along approach regions wider than the ordinary non-tangential cones. The sharp approach region, defined by means of a monotone function, increases with p. We make this picture complete by determining along which approach regions one has almost everywhere convergence for L∞ boundary functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 521 - 527
Copyright
Copyright © Australian Mathematical Society 1997

References

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